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Search: id:A115713
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| A115713 |
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A divide-and-conquer related triangle. |
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+0
4
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| 1, -1, 1, -4, 0, 1, 0, 0, -1, 1, 0, -4, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, -4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are A115634. Diagonal sums are A115714. Inverse is A115715.
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FORMULA
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G.f.: (1-x+xy)/(1-x^2*y^2)-4x^2/(1-x^2*y); (1, x)-(x, x)/2-(x, -x)/2-4(x^2, x^2) expressed in the notation of stretched Riordan arrays; Column k has g.f. x^k-(x(-x)^k+x^(k+1))/2-4x^(2k+2); T(n, k)=if(n=k, 1, 0) OR if(n=2k+2, -4, 0) OR if(n=k+1, -(1+(-1)^k)/2, 0);
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EXAMPLE
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Triangle begins
1,
-1, 1,
-4, 0, 1,
0, 0, -1, 1,
0, -4, 0, 0, 1,
0, 0, 0, 0, -1, 1,
0, 0, -4, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, -4, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1
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CROSSREFS
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Sequence in context: A013462 A101453 A128131 this_sequence A115633 A036859 A036861
Adjacent sequences: A115710 A115711 A115712 this_sequence A115714 A115715 A115716
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 29 2006
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